4. Partial Derivatives

Differentiability And Local Linearity — Quiz

Test your understanding of differentiability and local linearity with 5 practice questions.

Practice Questions

Question 1

What is the main idea of differentiability for a function of two variables at a point $(a,b)$?

Question 2

If a function of two variables is differentiable at a point, what must also be true there?

Question 3

Which formula gives the linearization of $f(x,y)$ at $(a,b)$?

Question 4

For a differentiable surface $z=f(x,y)$ at $(a,b,f(a,b))$, what does the tangent plane represent?

Question 5

If $f(x,y)=x^2y+3y$, what is $f_x(x,y)$?